Question: The sum of two numbers is $44$, and their difference is $24$. What are the two numbers?
Answer: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 44}$ ${x-y = 24}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 68 $ $ x = \dfrac{68}{2} $ ${x = 34}$ Now that you know ${x = 34}$ , plug it back into $ {x+y = 44}$ to find $y$ ${(34)}{ + y = 44}$ ${y = 10}$ You can also plug ${x = 34}$ into $ {x-y = 24}$ and get the same answer for $y$ ${(34)}{ - y = 24}$ ${y = 10}$ Therefore, the larger number is $34$, and the smaller number is $10$.